Questions: Find the amplitude (if one exists), period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods. y=-6 sin(3x + π/2) What is the amplitude? Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The amplitude is . (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. The function does not have an amplitude.

$Find the amplitude (if one exists), period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods. y=-6 sin(3x + π/2) What is the amplitude? Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The amplitude is . (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. The function does not have an amplitude.$

Transcript text: earson Pearson MyLab and Mastering mylab.pearson.com lus \& Trigonometry (Hybrid) Fall 2024 ework Sec 6.6 Question 3, 6.6.7 Part 1 of 4 Find the amplitude (if one exists), period, and phase shift of the function. Graph the function. Be sure to label key points. Show at least two periods. \[ y=-6 \sin \left(3 x+\frac{\pi}{2}\right) \] What is the amplitude? Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The amplitude is $\square$ . (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.) B. The function does not have an amplitude. View an example Get more help -

Solution

Solution Steps

Step 1: Determine the Amplitude

The amplitude of the function $ y = -6 \sin \left(3 x + \frac{\pi}{2}\right) $ is the absolute value of the coefficient of the sine function.

\[ \text{Amplitude} = | -6 | = 6 \]

Step 2: Determine the Period

The period of the sine function $ y = \sin(bx + c) $ is given by $ \frac{2\pi}{|b|} $. Here, $ b = 3 $.

\[ \text{Period} = \frac{2\pi}{3} \]

Step 3: Determine the Phase Shift

The phase shift of the function $ y = \sin(bx + c) $ is given by $ -\frac{c}{b} $. Here, $ c = \frac{\pi}{2} $ and $ b = 3 $.

\[ \text{Phase Shift} = -\frac{\frac{\pi}{2}}{3} = -\frac{\pi}{6} \]

Final Answer

Amplitude: $ 6 $
Period: $ \frac{2\pi}{3} $
Phase Shift: $ -\frac{\pi}{6} $

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